LMFDB - Embedded newform 147.4.a.m.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [147,4,Mod(1,147)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(147, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("147.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 147 = 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	147.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$8.67328077084$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.57516.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 24x + 6 $ x^3 - x^2 - 24*x + 6
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 21)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$0.248072$ of defining polynomial
Character	$\chi$	$=$	147.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.248072 q^{2} +3.00000 q^{3} -7.93846 q^{4} +12.4346 q^{5} +0.744216 q^{6} -3.95388 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+0.248072 q^{2} +3.00000 q^{3} -7.93846 q^{4} +12.4346 q^{5} +0.744216 q^{6} -3.95388 q^{8} +9.00000 q^{9} +3.08468 q^{10} +60.3115 q^{11} -23.8154 q^{12} -36.4269 q^{13} +37.3038 q^{15} +62.5268 q^{16} +48.7461 q^{17} +2.23265 q^{18} +50.5500 q^{19} -98.7116 q^{20} +14.9616 q^{22} +138.792 q^{23} -11.8617 q^{24} +29.6194 q^{25} -9.03649 q^{26} +27.0000 q^{27} -61.1345 q^{29} +9.25403 q^{30} +1.16935 q^{31} +47.1422 q^{32} +180.935 q^{33} +12.0925 q^{34} -71.4461 q^{36} +69.5268 q^{37} +12.5400 q^{38} -109.281 q^{39} -49.1650 q^{40} -308.115 q^{41} +174.443 q^{43} -478.781 q^{44} +111.911 q^{45} +34.4305 q^{46} -389.362 q^{47} +187.581 q^{48} +7.34774 q^{50} +146.238 q^{51} +289.173 q^{52} +314.935 q^{53} +6.69794 q^{54} +749.950 q^{55} +151.650 q^{57} -15.1657 q^{58} -844.526 q^{59} -296.135 q^{60} +338.538 q^{61} +0.290084 q^{62} -488.520 q^{64} -452.954 q^{65} +44.8848 q^{66} -971.550 q^{67} -386.969 q^{68} +416.377 q^{69} -98.4698 q^{71} -35.5850 q^{72} -710.235 q^{73} +17.2477 q^{74} +88.8581 q^{75} -401.289 q^{76} -27.1095 q^{78} -486.884 q^{79} +777.496 q^{80} +81.0000 q^{81} -76.4348 q^{82} -605.688 q^{83} +606.139 q^{85} +43.2743 q^{86} -183.403 q^{87} -238.465 q^{88} -218.069 q^{89} +27.7621 q^{90} -1101.80 q^{92} +3.50806 q^{93} -96.5897 q^{94} +628.569 q^{95} +141.427 q^{96} +782.288 q^{97} +542.804 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + q^{2} + 9 q^{3} + 25 q^{4} - 11 q^{5} + 3 q^{6} + 39 q^{8} + 27 q^{9}+O(q^{10}) $ 3 * q + q^2 + 9 * q^3 + 25 * q^4 - 11 * q^5 + 3 * q^6 + 39 * q^8 + 27 * q^9	\( 3 q + q^{2} + 9 q^{3} + 25 q^{4} - 11 q^{5} + 3 q^{6} + 39 q^{8} + 27 q^{9} + 55 q^{10} + 35 q^{11} + 75 q^{12} - 62 q^{13} - 33 q^{15} + 241 q^{16} - 48 q^{17} + 9 q^{18} + 202 q^{19} - 439 q^{20} - 7 q^{22} + 216 q^{23} + 117 q^{24} + 130 q^{25} - 274 q^{26} + 81 q^{27} + 53 q^{29} + 165 q^{30} + 95 q^{31} + 683 q^{32} + 105 q^{33} + 24 q^{34} + 225 q^{36} + 262 q^{37} + 398 q^{38} - 186 q^{39} - 21 q^{40} - 244 q^{41} + 360 q^{43} - 905 q^{44} - 99 q^{45} - 1056 q^{46} + 210 q^{47} + 723 q^{48} - 1378 q^{50} - 144 q^{51} - 324 q^{52} + 393 q^{53} + 27 q^{54} + 1031 q^{55} + 606 q^{57} - 1249 q^{58} - 1143 q^{59} - 1317 q^{60} + 70 q^{61} - 1059 q^{62} - 399 q^{64} - 472 q^{65} - 21 q^{66} - 628 q^{67} - 1944 q^{68} + 648 q^{69} + 318 q^{71} + 351 q^{72} - 988 q^{73} + 1002 q^{74} + 390 q^{75} + 2340 q^{76} - 822 q^{78} + 861 q^{79} - 175 q^{80} + 243 q^{81} - 124 q^{82} - 519 q^{83} + 1800 q^{85} - 3208 q^{86} + 159 q^{87} - 891 q^{88} - 1766 q^{89} + 495 q^{90} - 672 q^{92} + 285 q^{93} + 3294 q^{94} - 736 q^{95} + 2049 q^{96} - 19 q^{97} + 315 q^{99}+O(q^{100}) \) 3 * q + q^2 + 9 * q^3 + 25 * q^4 - 11 * q^5 + 3 * q^6 + 39 * q^8 + 27 * q^9 + 55 * q^10 + 35 * q^11 + 75 * q^12 - 62 * q^13 - 33 * q^15 + 241 * q^16 - 48 * q^17 + 9 * q^18 + 202 * q^19 - 439 * q^20 - 7 * q^22 + 216 * q^23 + 117 * q^24 + 130 * q^25 - 274 * q^26 + 81 * q^27 + 53 * q^29 + 165 * q^30 + 95 * q^31 + 683 * q^32 + 105 * q^33 + 24 * q^34 + 225 * q^36 + 262 * q^37 + 398 * q^38 - 186 * q^39 - 21 * q^40 - 244 * q^41 + 360 * q^43 - 905 * q^44 - 99 * q^45 - 1056 * q^46 + 210 * q^47 + 723 * q^48 - 1378 * q^50 - 144 * q^51 - 324 * q^52 + 393 * q^53 + 27 * q^54 + 1031 * q^55 + 606 * q^57 - 1249 * q^58 - 1143 * q^59 - 1317 * q^60 + 70 * q^61 - 1059 * q^62 - 399 * q^64 - 472 * q^65 - 21 * q^66 - 628 * q^67 - 1944 * q^68 + 648 * q^69 + 318 * q^71 + 351 * q^72 - 988 * q^73 + 1002 * q^74 + 390 * q^75 + 2340 * q^76 - 822 * q^78 + 861 * q^79 - 175 * q^80 + 243 * q^81 - 124 * q^82 - 519 * q^83 + 1800 * q^85 - 3208 * q^86 + 159 * q^87 - 891 * q^88 - 1766 * q^89 + 495 * q^90 - 672 * q^92 + 285 * q^93 + 3294 * q^94 - 736 * q^95 + 2049 * q^96 - 19 * q^97 + 315 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	0.248072	0.0877067	0.0438533	−	0.999038i	$-0.486037\pi$
$2$	0.248072	0.0877067	0.0438533	+	0.999038i	$0.486037\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	−7.93846	−0.992308
$5$	12.4346	1.11218	0.556092	−	0.831120i	$-0.312300\pi$
$5$	12.4346	1.11218	0.556092	+	0.831120i	$0.312300\pi$
$6$	0.744216	0.0506375
$7$	0	0
$7$	0	0
$8$	−3.95388	−0.174739
$9$	9.00000	0.333333
$10$	3.08468	0.0975460
$11$	60.3115	1.65315	0.826573	−	0.562829i	$-0.190287\pi$
$11$	60.3115	1.65315	0.826573	+	0.562829i	$0.190287\pi$
$12$	−23.8154	−0.572909
$13$	−36.4269	−0.777154	−0.388577	−	0.921416i	$-0.627033\pi$
$13$	−36.4269	−0.777154	−0.388577	+	0.921416i	$0.627033\pi$
$14$	0	0
$15$	37.3038	0.642120
$16$	62.5268	0.976982
$17$	48.7461	0.695451	0.347726	−	0.937596i	$-0.386954\pi$
$17$	48.7461	0.695451	0.347726	+	0.937596i	$0.386954\pi$
$18$	2.23265	0.0292356
$19$	50.5500	0.610366	0.305183	−	0.952294i	$-0.401282\pi$
$19$	50.5500	0.610366	0.305183	+	0.952294i	$0.401282\pi$
$20$	−98.7116	−1.10363
$21$	0	0
$22$	14.9616	0.144992
$23$	138.792	1.25827	0.629135	−	0.777296i	$-0.283409\pi$
$23$	138.792	1.25827	0.629135	+	0.777296i	$0.283409\pi$
$24$	−11.8617	−0.100885
$25$	29.6194	0.236955
$26$	−9.03649	−0.0681616
$27$	27.0000	0.192450
$28$	0	0
$29$	−61.1345	−0.391462	−0.195731	−	0.980658i	$-0.562708\pi$
$29$	−61.1345	−0.391462	−0.195731	+	0.980658i	$0.562708\pi$
$30$	9.25403	0.0563182
$31$	1.16935	0.00677490	0.00338745	−	0.999994i	$-0.498922\pi$
$31$	1.16935	0.00677490	0.00338745	+	0.999994i	$0.498922\pi$
$32$	47.1422	0.260426
$33$	180.935	0.954444
$34$	12.0925	0.0609957
$35$	0	0
$36$	−71.4461	−0.330769
$37$	69.5268	0.308923	0.154461	−	0.987999i	$-0.450636\pi$
$37$	69.5268	0.308923	0.154461	+	0.987999i	$0.450636\pi$
$38$	12.5400	0.0535332
$39$	−109.281	−0.448690
$40$	−49.1650	−0.194342
$41$	−308.115	−1.17365	−0.586823	−	0.809715i	$-0.699622\pi$
$41$	−308.115	−1.17365	−0.586823	+	0.809715i	$0.699622\pi$
$42$	0	0
$43$	174.443	0.618657	0.309329	−	0.950955i	$-0.399896\pi$
$43$	174.443	0.618657	0.309329	+	0.950955i	$0.399896\pi$
$44$	−478.781	−1.64043
$45$	111.911	0.370728
$46$	34.4305	0.110359
$47$	−389.362	−1.20839	−0.604194	−	0.796837i	$-0.706505\pi$
$47$	−389.362	−1.20839	−0.604194	+	0.796837i	$0.706505\pi$
$48$	187.581	0.564061
$49$	0	0
$50$	7.34774	0.0207825
$51$	146.238	0.401519
$52$	289.173	0.771176
$53$	314.935	0.816220	0.408110	−	0.912933i	$-0.366188\pi$
$53$	314.935	0.816220	0.408110	+	0.912933i	$0.366188\pi$
$54$	6.69794	0.0168792
$55$	749.950	1.83860
$56$	0	0
$57$	151.650	0.352395
$58$	−15.1657	−0.0343338
$59$	−844.526	−1.86352	−0.931762	−	0.363068i	$-0.881729\pi$
$59$	−844.526	−1.86352	−0.931762	+	0.363068i	$0.881729\pi$
$60$	−296.135	−0.637181
$61$	338.538	0.710579	0.355290	−	0.934756i	$-0.384382\pi$
$61$	338.538	0.710579	0.355290	+	0.934756i	$0.384382\pi$
$62$	0.290084	0.000594204 0
$63$	0	0
$64$	−488.520	−0.954141
$65$	−452.954	−0.864339
$66$	44.8848	0.0837111
$67$	−971.550	−1.77155	−0.885774	−	0.464117i	$-0.846372\pi$
$67$	−971.550	−1.77155	−0.885774	+	0.464117i	$0.846372\pi$
$68$	−386.969	−0.690102
$69$	416.377	0.726463
$70$	0	0
$71$	−98.4698	−0.164595	−0.0822973	−	0.996608i	$-0.526226\pi$
$71$	−98.4698	−0.164595	−0.0822973	+	0.996608i	$0.526226\pi$
$72$	−35.5850	−0.0582462
$73$	−710.235	−1.13872	−0.569361	−	0.822088i	$-0.692809\pi$
$73$	−710.235	−1.13872	−0.569361	+	0.822088i	$0.692809\pi$
$74$	17.2477	0.0270946
$75$	88.8581	0.136806
$76$	−401.289	−0.605671
$77$	0	0
$78$	−27.1095	−0.0393531
$79$	−486.884	−0.693402	−0.346701	−	0.937976i	$-0.612698\pi$
$79$	−486.884	−0.693402	−0.346701	+	0.937976i	$0.612698\pi$
$80$	777.496	1.08658
$81$	81.0000	0.111111
$82$	−76.4348	−0.102937
$83$	−605.688	−0.800999	−0.400499	−	0.916297i	$-0.631163\pi$
$83$	−605.688	−0.800999	−0.400499	+	0.916297i	$0.631163\pi$
$84$	0	0
$85$	606.139	0.773470
$86$	43.2743	0.0542604
$87$	−183.403	−0.226010
$88$	−238.465	−0.288869
$89$	−218.069	−0.259722	−0.129861	−	0.991532i	$-0.541453\pi$
$89$	−218.069	−0.259722	−0.129861	+	0.991532i	$0.541453\pi$
$90$	27.7621	0.0325153
$91$	0	0
$92$	−1101.80	−1.24859
$93$	3.50806	0.00391149
$94$	−96.5897	−0.105984
$95$	628.569	0.678840
$96$	141.427	0.150357
$97$	782.288	0.818859	0.409429	−	0.912342i	$-0.365728\pi$
$97$	782.288	0.818859	0.409429	+	0.912342i	$0.365728\pi$
$98$	0	0
$99$	542.804	0.551049
$100$	−235.132	−0.235132
$101$	311.646	0.307029	0.153514	−	0.988146i	$-0.450941\pi$
$101$	311.646	0.307029	0.153514	+	0.988146i	$0.450941\pi$
$102$	36.2776	0.0352159
$103$	149.258	0.142784	0.0713922	−	0.997448i	$-0.477256\pi$
$103$	149.258	0.142784	0.0713922	+	0.997448i	$0.477256\pi$
$104$	144.028	0.135799
$105$	0	0
$106$	78.1265	0.0715879
$107$	851.519	0.769341	0.384670	−	0.923054i	$-0.374315\pi$
$107$	851.519	0.769341	0.384670	+	0.923054i	$0.374315\pi$
$108$	−214.338	−0.190970
$109$	1361.88	1.19674	0.598369	−	0.801221i	$-0.295816\pi$
$109$	1361.88	1.19674	0.598369	+	0.801221i	$0.295816\pi$
$110$	186.042	0.161258
$111$	208.581	0.178357
$112$	0	0
$113$	1048.55	0.872917	0.436459	−	0.899724i	$-0.356233\pi$
$113$	1048.55	0.872917	0.436459	+	0.899724i	$0.356233\pi$
$114$	37.6201	0.0309074
$115$	1725.83	1.39943
$116$	485.313	0.388450
$117$	−327.842	−0.259051
$118$	−209.503	−0.163444
$119$	0	0
$120$	−147.495	−0.112203
$121$	2306.48	1.73289
$122$	83.9817	0.0623225
$123$	−924.346	−0.677605
$124$	−9.28286	−0.00672279
$125$	−1186.02	−0.848647
$126$	0	0
$127$	488.408	0.341254	0.170627	−	0.985336i	$-0.445421\pi$
$127$	488.408	0.341254	0.170627	+	0.985336i	$0.445421\pi$
$128$	−498.326	−0.344111
$129$	523.328	0.357182
$130$	−112.365	−0.0758083
$131$	1854.23	1.23668	0.618338	−	0.785912i	$-0.287806\pi$
$131$	1854.23	1.23668	0.618338	+	0.785912i	$0.287806\pi$
$132$	−1436.34	−0.947102
$133$	0	0
$134$	−241.014	−0.155377
$135$	335.734	0.214040
$136$	−192.737	−0.121522
$137$	−511.115	−0.318741	−0.159370	−	0.987219i	$-0.550946\pi$
$137$	−511.115	−0.318741	−0.159370	+	0.987219i	$0.550946\pi$
$138$	103.292	0.0637156
$139$	−2266.10	−1.38279	−0.691397	−	0.722475i	$-0.743005\pi$
$139$	−2266.10	−1.38279	−0.691397	+	0.722475i	$0.743005\pi$
$140$	0	0
$141$	−1168.09	−0.697663
$142$	−24.4276	−0.0144360
$143$	−2196.96	−1.28475
$144$	562.742	0.325661
$145$	−760.183	−0.435378
$146$	−176.189	−0.0998735
$147$	0	0
$148$	−551.936	−0.306546
$149$	1507.90	0.829074	0.414537	−	0.910033i	$-0.363944\pi$
$149$	1507.90	0.829074	0.414537	+	0.910033i	$0.363944\pi$
$150$	22.0432	0.0119988
$151$	1591.83	0.857887	0.428943	−	0.903331i	$-0.358886\pi$
$151$	1591.83	0.857887	0.428943	+	0.903331i	$0.358886\pi$
$152$	−199.869	−0.106655
$153$	438.715	0.231817
$154$	0	0
$155$	14.5404	0.00753494
$156$	867.520	0.445239
$157$	−1164.16	−0.591784	−0.295892	−	0.955221i	$-0.595617\pi$
$157$	−1164.16	−0.591784	−0.295892	+	0.955221i	$0.595617\pi$
$158$	−120.782	−0.0608160
$159$	944.805	0.471245
$160$	586.195	0.289642
$161$	0	0
$162$	20.0938	0.00974519
$163$	−1155.88	−0.555432	−0.277716	−	0.960663i	$-0.589577\pi$
$163$	−1155.88	−0.555432	−0.277716	+	0.960663i	$0.589577\pi$
$164$	2445.96	1.16462
$165$	2249.85	1.06152
$166$	−150.254	−0.0702529
$167$	2890.61	1.33941	0.669707	−	0.742626i	$-0.266420\pi$
$167$	2890.61	1.33941	0.669707	+	0.742626i	$0.266420\pi$
$168$	0	0
$169$	−870.082	−0.396032
$170$	150.366	0.0678385
$171$	454.950	0.203455
$172$	−1384.81	−0.613898
$173$	−1894.94	−0.832770	−0.416385	−	0.909188i	$-0.636703\pi$
$173$	−1894.94	−0.832770	−0.416385	+	0.909188i	$0.636703\pi$
$174$	−45.4972	−0.0198226
$175$	0	0
$176$	3771.09	1.61509
$177$	−2533.58	−1.07591
$178$	−54.0967	−0.0227793
$179$	−4288.49	−1.79071	−0.895355	−	0.445354i	$-0.853078\pi$
$179$	−4288.49	−1.79071	−0.895355	+	0.445354i	$0.853078\pi$
$180$	−888.405	−0.367876
$181$	−383.732	−0.157583	−0.0787917	−	0.996891i	$-0.525106\pi$
$181$	−383.732	−0.157583	−0.0787917	+	0.996891i	$0.525106\pi$
$182$	0	0
$183$	1015.61	0.410253
$184$	−548.769	−0.219868
$185$	864.539	0.343579
$186$	0.870251	0.000343064 0
$187$	2939.95	1.14968
$188$	3090.93	1.19909
$189$	0	0
$190$	155.930	0.0595388
$191$	385.311	0.145969	0.0729845	−	0.997333i	$-0.476748\pi$
$191$	385.311	0.145969	0.0729845	+	0.997333i	$0.476748\pi$
$192$	−1465.56	−0.550873
$193$	630.224	0.235049	0.117525	−	0.993070i	$-0.462504\pi$
$193$	630.224	0.235049	0.117525	+	0.993070i	$0.462504\pi$
$194$	194.064	0.0718194
$195$	−1358.86	−0.499026
$196$	0	0
$197$	−1250.23	−0.452158	−0.226079	−	0.974109i	$-0.572591\pi$
$197$	−1250.23	−0.452158	−0.226079	+	0.974109i	$0.572591\pi$
$198$	134.654	0.0483307
$199$	1092.24	0.389081	0.194541	−	0.980894i	$-0.437678\pi$
$199$	1092.24	0.389081	0.194541	+	0.980894i	$0.437678\pi$
$200$	−117.112	−0.0414052
$201$	−2914.65	−1.02280
$202$	77.3105	0.0269285
$203$	0	0
$204$	−1160.91	−0.398430
$205$	−3831.29	−1.30531
$206$	37.0267	0.0125232
$207$	1249.13	0.419423
$208$	−2277.66	−0.759265
$209$	3048.75	1.00902
$210$	0	0
$211$	−3620.05	−1.18111	−0.590556	−	0.806997i	$-0.701091\pi$
$211$	−3620.05	−1.18111	−0.590556	+	0.806997i	$0.701091\pi$
$212$	−2500.10	−0.809941
$213$	−295.409	−0.0950287
$214$	211.238	0.0674763
$215$	2169.13	0.688061
$216$	−106.755	−0.0336285
$217$	0	0
$218$	337.844	0.104962
$219$	−2130.70	−0.657442
$220$	−5953.45	−1.82446
$221$	−1775.67	−0.540473
$222$	51.7430	0.0156431
$223$	183.844	0.0552069	0.0276034	−	0.999619i	$-0.491212\pi$
$223$	183.844	0.0552069	0.0276034	+	0.999619i	$0.491212\pi$
$224$	0	0
$225$	266.574	0.0789850
$226$	260.117	0.0765607
$227$	−2279.52	−0.666506	−0.333253	−	0.942837i	$-0.608146\pi$
$227$	−2279.52	−0.666506	−0.333253	+	0.942837i	$0.608146\pi$
$228$	−1203.87	−0.349684
$229$	−5412.67	−1.56192	−0.780960	−	0.624582i	$-0.785270\pi$
$229$	−5412.67	−1.56192	−0.780960	+	0.624582i	$0.785270\pi$
$230$	428.130	0.122739
$231$	0	0
$232$	241.719	0.0684035
$233$	1138.37	0.320073	0.160036	−	0.987111i	$-0.448839\pi$
$233$	1138.37	0.320073	0.160036	+	0.987111i	$0.448839\pi$
$234$	−81.3284	−0.0227205
$235$	−4841.56	−1.34395
$236$	6704.24	1.84919
$237$	−1460.65	−0.400336
$238$	0	0
$239$	−6226.36	−1.68515	−0.842573	−	0.538583i	$-0.818960\pi$
$239$	−6226.36	−1.68515	−0.842573	+	0.538583i	$0.818960\pi$
$240$	2332.49	0.627340
$241$	3196.20	0.854295	0.427147	−	0.904182i	$-0.359519\pi$
$241$	3196.20	0.854295	0.427147	+	0.904182i	$0.359519\pi$
$242$	572.173	0.151986
$243$	243.000	0.0641500
$244$	−2687.47	−0.705113
$245$	0	0
$246$	−229.304	−0.0594305
$247$	−1841.38	−0.474349
$248$	−4.62349	−0.00118384
$249$	−1817.06	−0.462457
$250$	−294.218	−0.0744320
$251$	−239.608	−0.0602546	−0.0301273	−	0.999546i	$-0.509591\pi$
$251$	−239.608	−0.0602546	−0.0301273	+	0.999546i	$0.509591\pi$
$252$	0	0
$253$	8370.78	2.08010
$254$	121.160	0.0299302
$255$	1818.42	0.446563
$256$	3784.54	0.923960
$257$	−699.117	−0.169688	−0.0848439	−	0.996394i	$-0.527039\pi$
$257$	−699.117	−0.169688	−0.0848439	+	0.996394i	$0.527039\pi$
$258$	129.823	0.0313272
$259$	0	0
$260$	3595.76	0.857690
$261$	−550.210	−0.130487
$262$	459.982	0.108465
$263$	−919.040	−0.215477	−0.107738	−	0.994179i	$-0.534361\pi$
$263$	−919.040	−0.215477	−0.107738	+	0.994179i	$0.534361\pi$
$264$	−715.394	−0.166778
$265$	3916.09	0.907787
$266$	0	0
$267$	−654.206	−0.149950
$268$	7712.61	1.75792
$269$	2779.17	0.629923	0.314961	−	0.949104i	$-0.398008\pi$
$269$	2779.17	0.629923	0.314961	+	0.949104i	$0.398008\pi$
$270$	83.2863	0.0187727
$271$	−2226.98	−0.499186	−0.249593	−	0.968351i	$-0.580297\pi$
$271$	−2226.98	−0.499186	−0.249593	+	0.968351i	$0.580297\pi$
$272$	3047.94	0.679443
$273$	0	0
$274$	−126.793	−0.0279557
$275$	1786.39	0.391721
$276$	−3305.39	−0.720874
$277$	7307.69	1.58511	0.792557	−	0.609797i	$-0.208749\pi$
$277$	7307.69	1.58511	0.792557	+	0.609797i	$0.208749\pi$
$278$	−562.157	−0.121280
$279$	10.5242	0.00225830
$280$	0	0
$281$	2730.61	0.579696	0.289848	−	0.957073i	$-0.406395\pi$
$281$	2730.61	0.579696	0.289848	+	0.957073i	$0.406395\pi$
$282$	−289.769	−0.0611897
$283$	1769.85	0.371755	0.185878	−	0.982573i	$-0.440487\pi$
$283$	1769.85	0.371755	0.185878	+	0.982573i	$0.440487\pi$
$284$	781.698	0.163328
$285$	1885.71	0.391928
$286$	−545.004	−0.112681
$287$	0	0
$288$	424.280	0.0868088
$289$	−2536.81	−0.516347
$290$	−188.580	−0.0381855
$291$	2346.86	0.472768
$292$	5638.17	1.12996
$293$	−8228.81	−1.64072	−0.820362	−	0.571844i	$-0.806228\pi$
$293$	−8228.81	−1.64072	−0.820362	+	0.571844i	$0.806228\pi$
$294$	0	0
$295$	−10501.4	−2.07258
$296$	−274.901	−0.0539807
$297$	1628.41	0.318148
$298$	374.068	0.0727153
$299$	−5055.78	−0.977870
$300$	−705.397	−0.135754
$301$	0	0
$302$	394.887	0.0752424
$303$	934.937	0.177263
$304$	3160.73	0.596317
$305$	4209.58	0.790295
$306$	108.833	0.0203319
$307$	−6019.62	−1.11908	−0.559541	−	0.828803i	$-0.689023\pi$
$307$	−6019.62	−1.11908	−0.559541	+	0.828803i	$0.689023\pi$
$308$	0	0
$309$	447.773	0.0824366
$310$	3.60707	0.000660865 0
$311$	−1193.71	−0.217650	−0.108825	−	0.994061i	$-0.534709\pi$
$311$	−1193.71	−0.217650	−0.108825	+	0.994061i	$0.534709\pi$
$312$	432.083	0.0784035
$313$	8846.04	1.59747	0.798734	−	0.601684i	$-0.205503\pi$
$313$	8846.04	1.59747	0.798734	+	0.601684i	$0.205503\pi$
$314$	−288.795	−0.0519034
$315$	0	0
$316$	3865.11	0.688068
$317$	6081.43	1.07750	0.538750	−	0.842466i	$-0.318897\pi$
$317$	6081.43	1.07750	0.538750	+	0.842466i	$0.318897\pi$
$318$	234.380	0.0413313
$319$	−3687.11	−0.647143
$320$	−6074.55	−1.06118
$321$	2554.56	0.444179
$322$	0	0
$323$	2464.12	0.424480
$324$	−643.015	−0.110256
$325$	−1078.94	−0.184151
$326$	−286.741	−0.0487151
$327$	4085.64	0.690936
$328$	1218.25	0.205082
$329$	0	0
$330$	558.125	0.0931023
$331$	3053.30	0.507022	0.253511	−	0.967333i	$-0.418415\pi$
$331$	3053.30	0.507022	0.253511	+	0.967333i	$0.418415\pi$
$332$	4808.23	0.794837
$333$	625.742	0.102974
$334$	717.079	0.117475
$335$	−12080.8	−1.97029
$336$	0	0
$337$	3865.80	0.624877	0.312438	−	0.949938i	$-0.398854\pi$
$337$	3865.80	0.624877	0.312438	+	0.949938i	$0.398854\pi$
$338$	−215.843	−0.0347346
$339$	3145.66	0.503979
$340$	−4811.81	−0.767521
$341$	70.5255	0.0111999
$342$	112.860	0.0178444
$343$	0	0
$344$	−689.726	−0.108103
$345$	5177.49	0.807961
$346$	−470.080	−0.0730395
$347$	−99.5931	−0.0154076	−0.00770380	−	0.999970i	$-0.502452\pi$
$347$	−99.5931	−0.0154076	−0.00770380	+	0.999970i	$0.502452\pi$
$348$	1455.94	0.224272
$349$	3607.34	0.553285	0.276643	−	0.960973i	$-0.410778\pi$
$349$	3607.34	0.553285	0.276643	+	0.960973i	$0.410778\pi$
$350$	0	0
$351$	−983.526	−0.149563
$352$	2843.22	0.430523
$353$	−7130.73	−1.07516	−0.537579	−	0.843214i	$-0.680661\pi$
$353$	−7130.73	−1.07516	−0.537579	+	0.843214i	$0.680661\pi$
$354$	−628.510	−0.0943642
$355$	−1224.43	−0.183060
$356$	1731.13	0.257724
$357$	0	0
$358$	−1063.85	−0.157057
$359$	−6500.29	−0.955632	−0.477816	−	0.878460i	$-0.658572\pi$
$359$	−6500.29	−0.955632	−0.477816	+	0.878460i	$0.658572\pi$
$360$	−442.485	−0.0647806
$361$	−4303.70	−0.627453
$362$	−95.1932	−0.0138211
$363$	6919.44	1.00049
$364$	0	0
$365$	−8831.49	−1.26647
$366$	251.945	0.0359819
$367$	−824.886	−0.117326	−0.0586631	−	0.998278i	$-0.518684\pi$
$367$	−824.886	−0.117326	−0.0586631	+	0.998278i	$0.518684\pi$
$368$	8678.25	1.22931
$369$	−2773.04	−0.391216
$370$	214.468	0.0301342
$371$	0	0
$372$	−27.8486	−0.00388140
$373$	1333.85	0.185159	0.0925793	−	0.995705i	$-0.470489\pi$
$373$	1333.85	0.185159	0.0925793	+	0.995705i	$0.470489\pi$
$374$	729.320	0.100835
$375$	−3558.06	−0.489967
$376$	1539.49	0.211152
$377$	2226.94	0.304226
$378$	0	0
$379$	−1338.29	−0.181380	−0.0906902	−	0.995879i	$-0.528907\pi$
$379$	−1338.29	−0.181380	−0.0906902	+	0.995879i	$0.528907\pi$
$380$	−4989.87	−0.673618
$381$	1465.22	0.197023
$382$	95.5847	0.0128025
$383$	−353.376	−0.0471453	−0.0235727	−	0.999722i	$-0.507504\pi$
$383$	−353.376	−0.0471453	−0.0235727	+	0.999722i	$0.507504\pi$
$384$	−1494.98	−0.198673
$385$	0	0
$386$	156.341	0.0206154
$387$	1569.98	0.206219
$388$	−6210.16	−0.812560
$389$	11737.2	1.52982	0.764908	−	0.644139i	$-0.222784\pi$
$389$	11737.2	1.52982	0.764908	+	0.644139i	$0.222784\pi$
$390$	−337.096	−0.0437679
$391$	6765.59	0.875066
$392$	0	0
$393$	5562.68	0.713996
$394$	−310.147	−0.0396573
$395$	−6054.21	−0.771191
$396$	−4309.03	−0.546810
$397$	−13281.4	−1.67903	−0.839516	−	0.543335i	$-0.817161\pi$
$397$	−13281.4	−1.67903	−0.839516	+	0.543335i	$0.817161\pi$
$398$	270.955	0.0341250
$399$	0	0
$400$	1852.01	0.231501
$401$	−7482.36	−0.931798	−0.465899	−	0.884838i	$-0.654269\pi$
$401$	−7482.36	−0.931798	−0.465899	+	0.884838i	$0.654269\pi$
$402$	−723.043	−0.0897067
$403$	−42.5959	−0.00526514
$404$	−2473.99	−0.304667
$405$	1007.20	0.123576
$406$	0	0
$407$	4193.27	0.510694
$408$	−578.210	−0.0701609
$409$	13796.6	1.66797	0.833983	−	0.551791i	$-0.186055\pi$
$409$	13796.6	1.66797	0.833983	+	0.551791i	$0.186055\pi$
$410$	−950.436	−0.114485
$411$	−1533.35	−0.184025
$412$	−1184.88	−0.141686
$413$	0	0
$414$	309.875	0.0367862
$415$	−7531.49	−0.890859
$416$	−1717.24	−0.202391
$417$	−6798.31	−0.798357
$418$	756.308	0.0884982
$419$	−9497.56	−1.10737	−0.553683	−	0.832728i	$-0.686778\pi$
$419$	−9497.56	−1.10737	−0.553683	+	0.832728i	$0.686778\pi$
$420$	0	0
$421$	624.367	0.0722797	0.0361399	−	0.999347i	$-0.488494\pi$
$421$	624.367	0.0722797	0.0361399	+	0.999347i	$0.488494\pi$
$422$	−898.032	−0.103591
$423$	−3504.26	−0.402796
$424$	−1245.22	−0.142625
$425$	1443.83	0.164791
$426$	−73.2827	−0.00833465
$427$	0	0
$428$	−6759.75	−0.763423
$429$	−6590.88	−0.741750
$430$	538.099	0.0603475
$431$	−13397.3	−1.49727	−0.748636	−	0.662981i	$-0.769291\pi$
$431$	−13397.3	−1.49727	−0.748636	+	0.662981i	$0.769291\pi$
$432$	1688.22	0.188020
$433$	14057.3	1.56016	0.780079	−	0.625681i	$-0.215179\pi$
$433$	14057.3	1.56016	0.780079	+	0.625681i	$0.215179\pi$
$434$	0	0
$435$	−2280.55	−0.251365
$436$	−10811.2	−1.18753
$437$	7015.95	0.768006
$438$	−528.568	−0.0576620
$439$	16368.8	1.77960	0.889798	−	0.456356i	$-0.150845\pi$
$439$	16368.8	1.77960	0.889798	+	0.456356i	$0.150845\pi$
$440$	−2965.22	−0.321275
$441$	0	0
$442$	−440.494	−0.0474031
$443$	−1178.71	−0.126416	−0.0632078	−	0.998000i	$-0.520133\pi$
$443$	−1178.71	−0.126416	−0.0632078	+	0.998000i	$0.520133\pi$
$444$	−1655.81	−0.176985
$445$	−2711.60	−0.288858
$446$	45.6067	0.00484201
$447$	4523.70	0.478666
$448$	0	0
$449$	−12400.9	−1.30342	−0.651709	−	0.758469i	$-0.725948\pi$
$449$	−12400.9	−1.30342	−0.651709	+	0.758469i	$0.725948\pi$
$450$	66.1296	0.00692751
$451$	−18582.9	−1.94021
$452$	−8323.90	−0.866202
$453$	4775.48	0.495301
$454$	−565.484	−0.0584570
$455$	0	0
$456$	−599.606	−0.0615771
$457$	9925.58	1.01597	0.507986	−	0.861365i	$-0.330390\pi$
$457$	9925.58	1.01597	0.507986	+	0.861365i	$0.330390\pi$
$458$	−1342.73	−0.136991
$459$	1316.15	0.133840
$460$	−13700.4	−1.38866
$461$	16010.3	1.61751	0.808755	−	0.588146i	$-0.200142\pi$
$461$	16010.3	1.61751	0.808755	+	0.588146i	$0.200142\pi$
$462$	0	0
$463$	17372.4	1.74377	0.871883	−	0.489714i	$-0.162899\pi$
$463$	17372.4	1.74377	0.871883	+	0.489714i	$0.162899\pi$
$464$	−3822.54	−0.382451
$465$	43.6213	0.00435030
$466$	282.397	0.0280725
$467$	−2108.06	−0.208886	−0.104443	−	0.994531i	$-0.533306\pi$
$467$	−2108.06	−0.208886	−0.104443	+	0.994531i	$0.533306\pi$
$468$	2602.56	0.257059
$469$	0	0
$470$	−1201.05	−0.117873
$471$	−3492.48	−0.341667
$472$	3339.16	0.325630
$473$	10520.9	1.02273
$474$	−362.347	−0.0351121
$475$	1497.26	0.144629
$476$	0	0
$477$	2834.41	0.272073
$478$	−1544.59	−0.147798
$479$	2450.04	0.233706	0.116853	−	0.993149i	$-0.462719\pi$
$479$	2450.04	0.233706	0.116853	+	0.993149i	$0.462719\pi$
$480$	1758.58	0.167225
$481$	−2532.65	−0.240081
$482$	792.887	0.0749274
$483$	0	0
$484$	−18309.9	−1.71956
$485$	9727.44	0.910722
$486$	60.2815	0.00562639
$487$	645.236	0.0600379	0.0300189	−	0.999549i	$-0.490443\pi$
$487$	645.236	0.0600379	0.0300189	+	0.999549i	$0.490443\pi$
$488$	−1338.54	−0.124166
$489$	−3467.64	−0.320679
$490$	0	0
$491$	11766.1	1.08146	0.540731	−	0.841196i	$-0.318148\pi$
$491$	11766.1	1.08146	0.540731	+	0.841196i	$0.318148\pi$
$492$	7337.88	0.672393
$493$	−2980.07	−0.272242
$494$	−456.794	−0.0416035
$495$	6749.55	0.612868
$496$	73.1159	0.00661896
$497$	0	0
$498$	−450.763	−0.0405606
$499$	−44.0209	−0.00394919	−0.00197459	−	0.999998i	$-0.500629\pi$
$499$	−44.0209	−0.00394919	−0.00197459	+	0.999998i	$0.500629\pi$
$500$	9415.17	0.842119
$501$	8671.83	0.773311
$502$	−59.4399	−0.00528473
$503$	−8290.27	−0.734880	−0.367440	−	0.930047i	$-0.619766\pi$
$503$	−8290.27	−0.734880	−0.367440	+	0.930047i	$0.619766\pi$
$504$	0	0
$505$	3875.19	0.341473
$506$	2076.56	0.182439
$507$	−2610.24	−0.228649
$508$	−3877.21	−0.338629
$509$	−6915.04	−0.602168	−0.301084	−	0.953598i	$-0.597349\pi$
$509$	−6915.04	−0.602168	−0.301084	+	0.953598i	$0.597349\pi$
$510$	451.098	0.0391666
$511$	0	0
$512$	4925.45	0.425148
$513$	1364.85	0.117465
$514$	−173.431	−0.0148827
$515$	1855.96	0.158803
$516$	−4154.42	−0.354434
$517$	−23483.0	−1.99764
$518$	0	0
$519$	−5684.81	−0.480800
$520$	1790.93	0.151033
$521$	−13399.3	−1.12674	−0.563371	−	0.826204i	$-0.690496\pi$
$521$	−13399.3	−1.12674	−0.563371	+	0.826204i	$0.690496\pi$
$522$	−136.492	−0.0114446
$523$	9936.99	0.830811	0.415406	−	0.909636i	$-0.363640\pi$
$523$	9936.99	0.830811	0.415406	+	0.909636i	$0.363640\pi$
$524$	−14719.7	−1.22716
$525$	0	0
$526$	−227.988	−0.0188988
$527$	57.0014	0.00471161
$528$	11313.3	0.932475
$529$	7096.33	0.583244
$530$	971.472	0.0796190
$531$	−7600.74	−0.621175
$532$	0	0
$533$	11223.7	0.912104
$534$	−162.290	−0.0131516
$535$	10588.3	0.855649
$536$	3841.40	0.309558
$537$	−12865.5	−1.03387
$538$	689.435	0.0552484
$539$	0	0
$540$	−2665.21	−0.212394
$541$	9286.17	0.737973	0.368987	−	0.929435i	$-0.379705\pi$
$541$	9286.17	0.737973	0.368987	+	0.929435i	$0.379705\pi$
$542$	−552.452	−0.0437820
$543$	−1151.20	−0.0909809
$544$	2298.00	0.181114
$545$	16934.4	1.33099
$546$	0	0
$547$	−16821.6	−1.31488	−0.657438	−	0.753508i	$-0.728360\pi$
$547$	−16821.6	−1.31488	−0.657438	+	0.753508i	$0.728360\pi$
$548$	4057.47	0.316289
$549$	3046.84	0.236860
$550$	443.153	0.0343566
$551$	−3090.35	−0.238935
$552$	−1646.31	−0.126941
$553$	0	0
$554$	1812.83	0.139025
$555$	2593.62	0.198366
$556$	17989.4	1.37216
$557$	1805.94	0.137379	0.0686897	−	0.997638i	$-0.478118\pi$
$557$	1805.94	0.137379	0.0686897	+	0.997638i	$0.478118\pi$
$558$	2.61075	0.000198068 0
$559$	−6354.40	−0.480792
$560$	0	0
$561$	8819.86	0.663770
$562$	677.388	0.0508432
$563$	−12214.9	−0.914381	−0.457190	−	0.889369i	$-0.651144\pi$
$563$	−12214.9	−0.914381	−0.457190	+	0.889369i	$0.651144\pi$
$564$	9272.80	0.692296
$565$	13038.3	0.970845
$566$	439.050	0.0326054
$567$	0	0
$568$	389.338	0.0287610
$569$	4283.77	0.315615	0.157808	−	0.987470i	$-0.449557\pi$
$569$	4283.77	0.315615	0.157808	+	0.987470i	$0.449557\pi$
$570$	467.791	0.0343747
$571$	6359.94	0.466121	0.233060	−	0.972462i	$-0.425126\pi$
$571$	6359.94	0.466121	0.233060	+	0.972462i	$0.425126\pi$
$572$	17440.5	1.27487
$573$	1155.93	0.0842753
$574$	0	0
$575$	4110.95	0.298153
$576$	−4396.68	−0.318047
$577$	−14468.7	−1.04392	−0.521959	−	0.852971i	$-0.674799\pi$
$577$	−14468.7	−1.04392	−0.521959	+	0.852971i	$0.674799\pi$
$578$	−629.313	−0.0452871
$579$	1890.67	0.135706
$580$	6034.68	0.432028
$581$	0	0
$582$	582.191	0.0414649
$583$	18994.2	1.34933
$584$	2808.19	0.198979
$585$	−4076.59	−0.288113
$586$	−2041.34	−0.143903
$587$	11132.6	0.782777	0.391388	−	0.920226i	$-0.371995\pi$
$587$	11132.6	0.782777	0.391388	+	0.920226i	$0.371995\pi$
$588$	0	0
$589$	59.1108	0.00413517
$590$	−2605.09	−0.181779
$591$	−3750.69	−0.261054
$592$	4347.29	0.301812
$593$	19775.6	1.36946	0.684728	−	0.728799i	$-0.259921\pi$
$593$	19775.6	1.36946	0.684728	+	0.728799i	$0.259921\pi$
$594$	403.963	0.0279037
$595$	0	0
$596$	−11970.4	−0.822696
$597$	3276.73	0.224636
$598$	−1254.20	−0.0857657
$599$	−23891.0	−1.62965	−0.814825	−	0.579707i	$-0.803167\pi$
$599$	−23891.0	−1.62965	−0.814825	+	0.579707i	$0.803167\pi$
$600$	−351.335	−0.0239053
$601$	−19395.5	−1.31641	−0.658204	−	0.752840i	$-0.728683\pi$
$601$	−19395.5	−1.31641	−0.658204	+	0.752840i	$0.728683\pi$
$602$	0	0
$603$	−8743.95	−0.590516
$604$	−12636.6	−0.851288
$605$	28680.2	1.92730
$606$	231.932	0.0155472
$607$	−14596.7	−0.976051	−0.488025	−	0.872829i	$-0.662283\pi$
$607$	−14596.7	−0.976051	−0.488025	+	0.872829i	$0.662283\pi$
$608$	2383.04	0.158956
$609$	0	0
$610$	1044.28	0.0693142
$611$	14183.2	0.939104
$612$	−3482.72	−0.230034
$613$	1979.80	0.130446	0.0652229	−	0.997871i	$-0.479224\pi$
$613$	1979.80	0.130446	0.0652229	+	0.997871i	$0.479224\pi$
$614$	−1493.30	−0.0981509
$615$	−11493.9	−0.753622
$616$	0	0
$617$	16262.4	1.06110	0.530551	−	0.847653i	$-0.321985\pi$
$617$	16262.4	1.06110	0.530551	+	0.847653i	$0.321985\pi$
$618$	111.080	0.00723024
$619$	12021.0	0.780555	0.390278	−	0.920697i	$-0.372379\pi$
$619$	12021.0	0.780555	0.390278	+	0.920697i	$0.372379\pi$
$620$	−115.429	−0.00747698
$621$	3747.39	0.242154
$622$	−296.127	−0.0190894
$623$	0	0
$624$	−6832.97	−0.438362
$625$	−18450.1	−1.18081
$626$	2194.45	0.140109
$627$	9146.24	0.582561
$628$	9241.64	0.587232
$629$	3389.16	0.214841
$630$	0	0
$631$	25347.6	1.59916	0.799582	−	0.600557i	$-0.205055\pi$
$631$	25347.6	1.59916	0.799582	+	0.600557i	$0.205055\pi$
$632$	1925.08	0.121164
$633$	−10860.1	−0.681915
$634$	1508.63	0.0945039
$635$	6073.16	0.379537
$636$	−7500.29	−0.467620
$637$	0	0
$638$	−914.669	−0.0567588
$639$	−886.228	−0.0548648
$640$	−6196.49	−0.382715
$641$	−5111.60	−0.314971	−0.157485	−	0.987521i	$-0.550339\pi$
$641$	−5111.60	−0.314971	−0.157485	+	0.987521i	$0.550339\pi$
$642$	633.714	0.0389575
$643$	10931.3	0.670435	0.335217	−	0.942141i	$-0.391190\pi$
$643$	10931.3	0.670435	0.335217	+	0.942141i	$0.391190\pi$
$644$	0	0
$645$	6507.38	0.397252
$646$	611.278	0.0372297
$647$	18406.1	1.11842	0.559211	−	0.829025i	$-0.311104\pi$
$647$	18406.1	1.11842	0.559211	+	0.829025i	$0.311104\pi$
$648$	−320.265	−0.0194154
$649$	−50934.7	−3.08068
$650$	−267.655	−0.0161512
$651$	0	0
$652$	9175.91	0.551160
$653$	19921.4	1.19385	0.596926	−	0.802296i	$-0.296389\pi$
$653$	19921.4	1.19385	0.596926	+	0.802296i	$0.296389\pi$
$654$	1013.53	0.0605997
$655$	23056.6	1.37541
$656$	−19265.5	−1.14663
$657$	−6392.11	−0.379574
$658$	0	0
$659$	−18858.8	−1.11477	−0.557385	−	0.830254i	$-0.688195\pi$
$659$	−18858.8	−1.11477	−0.557385	+	0.830254i	$0.688195\pi$
$660$	−17860.3	−1.05335
$661$	−25832.1	−1.52005	−0.760023	−	0.649896i	$-0.774812\pi$
$661$	−25832.1	−1.52005	−0.760023	+	0.649896i	$0.774812\pi$
$662$	757.437	0.0444692
$663$	−5327.01	−0.312042
$664$	2394.82	0.139965
$665$	0	0
$666$	155.229	0.00903153
$667$	−8485.00	−0.492564
$668$	−22947.0	−1.32911
$669$	551.533	0.0318737
$670$	−2996.92	−0.172807
$671$	20417.7	1.17469
$672$	0	0
$673$	−16275.0	−0.932178	−0.466089	−	0.884738i	$-0.654337\pi$
$673$	−16275.0	−0.932178	−0.466089	+	0.884738i	$0.654337\pi$
$674$	958.996	0.0548059
$675$	799.723	0.0456020
$676$	6907.11	0.392985
$677$	26271.8	1.49144	0.745720	−	0.666259i	$-0.232105\pi$
$677$	26271.8	1.49144	0.745720	+	0.666259i	$0.232105\pi$
$678$	780.350	0.0442023
$679$	0	0
$680$	−2396.60	−0.135155
$681$	−6838.55	−0.384808
$682$	17.4954	0.000982306 0
$683$	−8072.29	−0.452237	−0.226118	−	0.974100i	$-0.572604\pi$
$683$	−8072.29	−0.452237	−0.226118	+	0.974100i	$0.572604\pi$
$684$	−3611.60	−0.201890
$685$	−6355.51	−0.354499
$686$	0	0
$687$	−16238.0	−0.901774
$688$	10907.3	0.604417
$689$	−11472.1	−0.634328
$690$	1284.39	0.0708636
$691$	24485.3	1.34799	0.673997	−	0.738734i	$-0.264576\pi$
$691$	24485.3	1.34799	0.673997	+	0.738734i	$0.264576\pi$
$692$	15042.9	0.826364
$693$	0	0
$694$	−24.7062	−0.00135135
$695$	−28178.1	−1.53792
$696$	725.156	0.0394928
$697$	−15019.4	−0.816214
$698$	894.880	0.0485268
$699$	3415.10	0.184794
$700$	0	0
$701$	778.448	0.0419423	0.0209712	−	0.999780i	$-0.493324\pi$
$701$	778.448	0.0419423	0.0209712	+	0.999780i	$0.493324\pi$
$702$	−243.985	−0.0131177
$703$	3514.58	0.188556
$704$	−29463.4	−1.57733
$705$	−14524.7	−0.775930
$706$	−1768.93	−0.0942985
$707$	0	0
$708$	20112.7	1.06763
$709$	−24172.0	−1.28039	−0.640197	−	0.768211i	$-0.721147\pi$
$709$	−24172.0	−1.28039	−0.640197	+	0.768211i	$0.721147\pi$
$710$	−303.747	−0.0160555
$711$	−4381.96	−0.231134
$712$	862.218	0.0453834
$713$	162.297	0.00852466
$714$	0	0
$715$	−27318.3	−1.42888
$716$	34044.0	1.77693
$717$	−18679.1	−0.972919
$718$	−1612.54	−0.0838153
$719$	81.8835	0.00424720	0.00212360	−	0.999998i	$-0.499324\pi$
$719$	81.8835	0.00424720	0.00212360	+	0.999998i	$0.499324\pi$
$720$	6997.47	0.362195
$721$	0	0
$722$	−1067.63	−0.0550318
$723$	9588.59	0.493227
$724$	3046.24	0.156371
$725$	−1810.76	−0.0927588
$726$	1716.52	0.0877493
$727$	32542.9	1.66018	0.830088	−	0.557632i	$-0.188290\pi$
$727$	32542.9	1.66018	0.830088	+	0.557632i	$0.188290\pi$
$728$	0	0
$729$	729.000	0.0370370
$730$	−2190.85	−0.111078
$731$	8503.40	0.430246
$732$	−8062.41	−0.407097
$733$	5068.94	0.255424	0.127712	−	0.991811i	$-0.459237\pi$
$733$	5068.94	0.255424	0.127712	+	0.991811i	$0.459237\pi$
$734$	−204.631	−0.0102903
$735$	0	0
$736$	6542.98	0.327687
$737$	−58595.6	−2.92863
$738$	−687.913	−0.0343122
$739$	−38428.5	−1.91287	−0.956437	−	0.291939i	$-0.905700\pi$
$739$	−38428.5	−1.91287	−0.956437	+	0.291939i	$0.905700\pi$
$740$	−6863.11	−0.340936
$741$	−5524.14	−0.273865
$742$	0	0
$743$	21592.9	1.06617	0.533086	−	0.846061i	$-0.321032\pi$
$743$	21592.9	1.06617	0.533086	+	0.846061i	$0.321032\pi$
$744$	−13.8705	−0.000683489 0
$745$	18750.1	0.922083
$746$	330.891	0.0162396
$747$	−5451.19	−0.267000
$748$	−23338.7	−1.14084
$749$	0	0
$750$	−882.655	−0.0429733
$751$	8112.60	0.394185	0.197093	−	0.980385i	$-0.436850\pi$
$751$	8112.60	0.394185	0.197093	+	0.980385i	$0.436850\pi$
$752$	−24345.6	−1.18057
$753$	−718.823	−0.0347880
$754$	552.441	0.0266826
$755$	19793.7	0.954129
$756$	0	0
$757$	3108.01	0.149224	0.0746120	−	0.997213i	$-0.476228\pi$
$757$	3108.01	0.149224	0.0746120	+	0.997213i	$0.476228\pi$
$758$	−331.992	−0.0159083
$759$	25112.3	1.20095
$760$	−2485.29	−0.118620
$761$	7211.93	0.343538	0.171769	−	0.985137i	$-0.445052\pi$
$761$	7211.93	0.343538	0.171769	+	0.985137i	$0.445052\pi$
$762$	363.481	0.0172802
$763$	0	0
$764$	−3058.77	−0.144846
$765$	5455.25	0.257823
$766$	−87.6626	−0.00413496
$767$	30763.5	1.44825
$768$	11353.6	0.533448
$769$	7533.07	0.353250	0.176625	−	0.984278i	$-0.443482\pi$
$769$	7533.07	0.353250	0.176625	+	0.984278i	$0.443482\pi$
$770$	0	0
$771$	−2097.35	−0.0979693
$772$	−5003.00	−0.233241
$773$	24832.6	1.15546	0.577728	−	0.816229i	$-0.303940\pi$
$773$	24832.6	1.15546	0.577728	+	0.816229i	$0.303940\pi$
$774$	389.469	0.0180868
$775$	34.6355	0.00160535
$776$	−3093.08	−0.143086
$777$	0	0
$778$	2911.66	0.134175
$779$	−15575.2	−0.716355
$780$	10787.3	0.495188
$781$	−5938.86	−0.272099
$782$	1678.35	0.0767491
$783$	−1650.63	−0.0753368
$784$	0	0
$785$	−14475.9	−0.658173
$786$	1379.95	0.0626222
$787$	−36313.1	−1.64476	−0.822378	−	0.568941i	$-0.807353\pi$
$787$	−36313.1	−1.64476	−0.822378	+	0.568941i	$0.807353\pi$
$788$	9924.89	0.448680
$789$	−2757.12	−0.124406
$790$	−1501.88	−0.0676386
$791$	0	0
$792$	−2146.18	−0.0962895
$793$	−12331.9	−0.552229
$794$	−3294.75	−0.147262
$795$	11748.3	0.524111
$796$	−8670.74	−0.386088
$797$	−31665.7	−1.40735	−0.703675	−	0.710522i	$-0.748459\pi$
$797$	−31665.7	−1.40735	−0.703675	+	0.710522i	$0.748459\pi$
$798$	0	0
$799$	−18979.9	−0.840375
$800$	1396.32	0.0617094
$801$	−1962.62	−0.0865738
$802$	−1856.16	−0.0817249
$803$	−42835.4	−1.88247
$804$	23137.8	1.01494
$805$	0	0
$806$	−10.5668	−0.000461788 0
$807$	8337.52	0.363686
$808$	−1232.21	−0.0536498
$809$	12384.6	0.538219	0.269110	−	0.963110i	$-0.413271\pi$
$809$	12384.6	0.538219	0.269110	+	0.963110i	$0.413271\pi$
$810$	249.859	0.0108384
$811$	−16742.4	−0.724914	−0.362457	−	0.932000i	$-0.618062\pi$
$811$	−16742.4	−0.724914	−0.362457	+	0.932000i	$0.618062\pi$
$812$	0	0
$813$	−6680.94	−0.288205
$814$	1040.23	0.0447913
$815$	−14372.9	−0.617744
$816$	9143.82	0.392277
$817$	8818.07	0.377607
$818$	3422.55	0.146292
$819$	0	0
$820$	30414.6	1.29527
$821$	26456.3	1.12464	0.562322	−	0.826918i	$-0.309908\pi$
$821$	26456.3	1.12464	0.562322	+	0.826918i	$0.309908\pi$
$822$	−380.380	−0.0161402
$823$	23098.5	0.978328	0.489164	−	0.872192i	$-0.337302\pi$
$823$	23098.5	0.978328	0.489164	+	0.872192i	$0.337302\pi$
$824$	−590.148	−0.0249500
$825$	5359.17	0.226160
$826$	0	0
$827$	20647.6	0.868183	0.434092	−	0.900869i	$-0.357069\pi$
$827$	20647.6	0.868183	0.434092	+	0.900869i	$0.357069\pi$
$828$	−9916.18	−0.416197
$829$	23368.5	0.979037	0.489519	−	0.871993i	$-0.337173\pi$
$829$	23368.5	0.979037	0.489519	+	0.871993i	$0.337173\pi$
$830$	−1868.35	−0.0781343
$831$	21923.1	0.915166
$832$	17795.3	0.741514
$833$	0	0
$834$	−1686.47	−0.0700212
$835$	35943.6	1.48968
$836$	−24202.3	−1.00126
$837$	31.5725	0.00130383
$838$	−2356.08	−0.0971234
$839$	−16735.5	−0.688645	−0.344322	−	0.938851i	$-0.611891\pi$
$839$	−16735.5	−0.688645	−0.344322	+	0.938851i	$0.611891\pi$
$840$	0	0
$841$	−20651.6	−0.846758
$842$	154.888	0.00633941
$843$	8191.84	0.334688
$844$	28737.6	1.17203
$845$	−10819.1	−0.440460
$846$	−869.307	−0.0353279
$847$	0	0
$848$	19691.9	0.797432
$849$	5309.55	0.214633
$850$	358.174	0.0144532
$851$	9649.80	0.388708
$852$	2345.09	0.0942977
$853$	10294.5	0.413219	0.206609	−	0.978424i	$-0.433757\pi$
$853$	10294.5	0.413219	0.206609	+	0.978424i	$0.433757\pi$
$854$	0	0
$855$	5657.12	0.226280
$856$	−3366.81	−0.134434
$857$	32788.6	1.30693	0.653463	−	0.756958i	$-0.273315\pi$
$857$	32788.6	1.30693	0.653463	+	0.756958i	$0.273315\pi$
$858$	−1635.01	−0.0650565
$859$	4909.76	0.195016	0.0975081	−	0.995235i	$-0.468913\pi$
$859$	4909.76	0.195016	0.0975081	+	0.995235i	$0.468913\pi$
$860$	−17219.5	−0.682768
$861$	0	0
$862$	−3323.49	−0.131321
$863$	17795.0	0.701909	0.350954	−	0.936393i	$-0.385857\pi$
$863$	17795.0	0.701909	0.350954	+	0.936393i	$0.385857\pi$
$864$	1272.84	0.0501191
$865$	−23562.8	−0.926195
$866$	3487.21	0.136836
$867$	−7610.44	−0.298113
$868$	0	0
$869$	−29364.7	−1.14629
$870$	−565.740	−0.0220464
$871$	35390.5	1.37677
$872$	−5384.71	−0.209116
$873$	7040.59	0.272953
$874$	1740.46	0.0673592
$875$	0	0
$876$	16914.5	0.652384
$877$	34672.2	1.33500	0.667501	−	0.744609i	$-0.267364\pi$
$877$	34672.2	1.33500	0.667501	+	0.744609i	$0.267364\pi$
$878$	4060.65	0.156082
$879$	−24686.4	−0.947273
$880$	46892.0	1.79628
$881$	−40848.2	−1.56210	−0.781051	−	0.624467i	$-0.785316\pi$
$881$	−40848.2	−1.56210	−0.781051	+	0.624467i	$0.785316\pi$
$882$	0	0
$883$	30035.1	1.14469	0.572345	−	0.820013i	$-0.306034\pi$
$883$	30035.1	1.14469	0.572345	+	0.820013i	$0.306034\pi$
$884$	14096.1	0.536315
$885$	−31504.1	−1.19661
$886$	−292.404	−0.0110875
$887$	−33210.7	−1.25717	−0.628583	−	0.777742i	$-0.716365\pi$
$887$	−33210.7	−1.25717	−0.628583	+	0.777742i	$0.716365\pi$
$888$	−824.703	−0.0311658
$889$	0	0
$890$	−672.671	−0.0253348
$891$	4885.23	0.183683
$892$	−1459.44	−0.0547822
$893$	−19682.2	−0.737559
$894$	1122.20	0.0419822
$895$	−53325.7	−1.99160
$896$	0	0
$897$	−15167.3	−0.564573
$898$	−3076.32	−0.114318
$899$	−71.4878	−0.00265211
$900$	−2116.19	−0.0783774
$901$	15351.9	0.567641
$902$	−4609.90	−0.170169
$903$	0	0
$904$	−4145.86	−0.152532
$905$	−4771.56	−0.175262
$906$	1184.66	0.0434412
$907$	2497.83	0.0914433	0.0457217	−	0.998954i	$-0.485441\pi$
$907$	2497.83	0.0914433	0.0457217	+	0.998954i	$0.485441\pi$
$908$	18095.9	0.661379
$909$	2804.81	0.102343
$910$	0	0
$911$	−1895.00	−0.0689180	−0.0344590	−	0.999406i	$-0.510971\pi$
$911$	−1895.00	−0.0689180	−0.0344590	+	0.999406i	$0.510971\pi$
$912$	9482.19	0.344284
$913$	−36530.0	−1.32417
$914$	2462.26	0.0891075
$915$	12628.8	0.456277
$916$	42968.3	1.54990
$917$	0	0
$918$	326.499	0.0117386
$919$	6270.71	0.225083	0.112542	−	0.993647i	$-0.464101\pi$
$919$	6270.71	0.225083	0.112542	+	0.993647i	$0.464101\pi$
$920$	−6823.73	−0.244534
$921$	−18058.9	−0.646102
$922$	3971.69	0.141866
$923$	3586.95	0.127915
$924$	0	0
$925$	2059.34	0.0732008
$926$	4309.61	0.152940
$927$	1343.32	0.0475948
$928$	−2882.01	−0.101947
$929$	31552.6	1.11432	0.557161	−	0.830404i	$-0.311890\pi$
$929$	31552.6	1.11432	0.557161	+	0.830404i	$0.311890\pi$
$930$	10.8212	0.000381550 0
$931$	0	0
$932$	−9036.89	−0.317611
$933$	−3581.14	−0.125661
$934$	−522.951	−0.0183207
$935$	36557.2	1.27866
$936$	1296.25	0.0452663
$937$	22030.2	0.768084	0.384042	−	0.923316i	$-0.374532\pi$
$937$	22030.2	0.768084	0.384042	+	0.923316i	$0.374532\pi$
$938$	0	0
$939$	26538.1	0.922299
$940$	38434.5	1.33361
$941$	32538.6	1.12724	0.563618	−	0.826036i	$-0.309409\pi$
$941$	32538.6	1.12724	0.563618	+	0.826036i	$0.309409\pi$
$942$	−866.386	−0.0299664
$943$	−42764.1	−1.47677
$944$	−52805.6	−1.82063
$945$	0	0
$946$	2609.94	0.0897003
$947$	−40711.0	−1.39697	−0.698485	−	0.715625i	$-0.746142\pi$
$947$	−40711.0	−1.39697	−0.698485	+	0.715625i	$0.746142\pi$
$948$	11595.3	0.397256
$949$	25871.7	0.884962
$950$	371.428	0.0126850
$951$	18244.3	0.622095
$952$	0	0
$953$	−52516.4	−1.78507	−0.892536	−	0.450976i	$-0.851076\pi$
$953$	−52516.4	−1.78507	−0.892536	+	0.450976i	$0.851076\pi$
$954$	703.139	0.0238626
$955$	4791.18	0.162345
$956$	49427.7	1.67218
$957$	−11061.3	−0.373628
$958$	607.786	0.0204976
$959$	0	0
$960$	−18223.7	−0.612673
$961$	−29789.6	−0.999954
$962$	−628.279	−0.0210567
$963$	7663.67	0.256447
$964$	−25372.9	−0.847723
$965$	7836.58	0.261418
$966$	0	0
$967$	14721.6	0.489570	0.244785	−	0.969577i	$-0.421283\pi$
$967$	14721.6	0.489570	0.244785	+	0.969577i	$0.421283\pi$
$968$	−9119.56	−0.302803
$969$	7392.35	0.245074
$970$	2413.10	0.0798764
$971$	−13772.5	−0.455181	−0.227590	−	0.973757i	$-0.573085\pi$
$971$	−13772.5	−0.455181	−0.227590	+	0.973757i	$0.573085\pi$
$972$	−1929.05	−0.0636566
$973$	0	0
$974$	160.065	0.00526572
$975$	−3236.83	−0.106319
$976$	21167.7	0.694223
$977$	24782.1	0.811513	0.405757	−	0.913981i	$-0.367008\pi$
$977$	24782.1	0.811513	0.405757	+	0.913981i	$0.367008\pi$
$978$	−860.224	−0.0281257
$979$	−13152.0	−0.429358
$980$	0	0
$981$	12256.9	0.398912
$982$	2918.84	0.0948514
$983$	−42804.7	−1.38887	−0.694435	−	0.719556i	$-0.744345\pi$
$983$	−42804.7	−1.38887	−0.694435	+	0.719556i	$0.744345\pi$
$984$	3654.76	0.118404
$985$	−15546.1	−0.502883
$986$	−739.271	−0.0238775
$987$	0	0
$988$	14617.7	0.470700
$989$	24211.3	0.778438
$990$	1674.37	0.0537526
$991$	449.862	0.0144201	0.00721006	−	0.999974i	$-0.497705\pi$
$991$	449.862	0.0144201	0.00721006	+	0.999974i	$0.497705\pi$
$992$	55.1259	0.00176436
$993$	9159.89	0.292729
$994$	0	0
$995$	13581.6	0.432730
$996$	14424.7	0.458899
$997$	21473.7	0.682127	0.341063	−	0.940040i	$-0.389213\pi$
$997$	21473.7	0.682127	0.341063	+	0.940040i	$0.389213\pi$
$998$	−10.9203	−0.000346370 0
$999$	1877.22	0.0594522

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.4.a.m.1.2		3
3.2	odd	2		441.4.a.t.1.2		3
4.3	odd	2		2352.4.a.cg.1.3		3
7.2	even	3		147.4.e.n.67.2		6
7.3	odd	6		21.4.e.b.16.2	yes	6
7.4	even	3		147.4.e.n.79.2		6
7.5	odd	6		21.4.e.b.4.2	✓	6
7.6	odd	2		147.4.a.l.1.2		3
21.2	odd	6		441.4.e.w.361.2		6
21.5	even	6		63.4.e.c.46.2		6
21.11	odd	6		441.4.e.w.226.2		6
21.17	even	6		63.4.e.c.37.2		6
21.20	even	2		441.4.a.s.1.2		3
28.3	even	6		336.4.q.k.289.3		6
28.19	even	6		336.4.q.k.193.3		6
28.27	even	2		2352.4.a.ci.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.4.e.b.4.2	✓	6	7.5	odd	6
21.4.e.b.16.2	yes	6	7.3	odd	6
63.4.e.c.37.2		6	21.17	even	6
63.4.e.c.46.2		6	21.5	even	6
147.4.a.l.1.2		3	7.6	odd	2
147.4.a.m.1.2		3	1.1	even	1	trivial
147.4.e.n.67.2		6	7.2	even	3
147.4.e.n.79.2		6	7.4	even	3
336.4.q.k.193.3		6	28.19	even	6
336.4.q.k.289.3		6	28.3	even	6
441.4.a.s.1.2		3	21.20	even	2
441.4.a.t.1.2		3	3.2	odd	2
441.4.e.w.226.2		6	21.11	odd	6
441.4.e.w.361.2		6	21.2	odd	6
2352.4.a.cg.1.3		3	4.3	odd	2
2352.4.a.ci.1.1		3	28.27	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	147.a (trivial)

\(f(q)\)	\(=\)	\(q+0.248072 q^{2} +3.00000 q^{3} -7.93846 q^{4} +12.4346 q^{5} +0.744216 q^{6} -3.95388 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+0.248072 q^{2} +3.00000 q^{3} -7.93846 q^{4} +12.4346 q^{5} +0.744216 q^{6} -3.95388 q^{8} +9.00000 q^{9} +3.08468 q^{10} +60.3115 q^{11} -23.8154 q^{12} -36.4269 q^{13} +37.3038 q^{15} +62.5268 q^{16} +48.7461 q^{17} +2.23265 q^{18} +50.5500 q^{19} -98.7116 q^{20} +14.9616 q^{22} +138.792 q^{23} -11.8617 q^{24} +29.6194 q^{25} -9.03649 q^{26} +27.0000 q^{27} -61.1345 q^{29} +9.25403 q^{30} +1.16935 q^{31} +47.1422 q^{32} +180.935 q^{33} +12.0925 q^{34} -71.4461 q^{36} +69.5268 q^{37} +12.5400 q^{38} -109.281 q^{39} -49.1650 q^{40} -308.115 q^{41} +174.443 q^{43} -478.781 q^{44} +111.911 q^{45} +34.4305 q^{46} -389.362 q^{47} +187.581 q^{48} +7.34774 q^{50} +146.238 q^{51} +289.173 q^{52} +314.935 q^{53} +6.69794 q^{54} +749.950 q^{55} +151.650 q^{57} -15.1657 q^{58} -844.526 q^{59} -296.135 q^{60} +338.538 q^{61} +0.290084 q^{62} -488.520 q^{64} -452.954 q^{65} +44.8848 q^{66} -971.550 q^{67} -386.969 q^{68} +416.377 q^{69} -98.4698 q^{71} -35.5850 q^{72} -710.235 q^{73} +17.2477 q^{74} +88.8581 q^{75} -401.289 q^{76} -27.1095 q^{78} -486.884 q^{79} +777.496 q^{80} +81.0000 q^{81} -76.4348 q^{82} -605.688 q^{83} +606.139 q^{85} +43.2743 q^{86} -183.403 q^{87} -238.465 q^{88} -218.069 q^{89} +27.7621 q^{90} -1101.80 q^{92} +3.50806 q^{93} -96.5897 q^{94} +628.569 q^{95} +141.427 q^{96} +782.288 q^{97} +542.804 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + q^{2} + 9 q^{3} + 25 q^{4} - 11 q^{5} + 3 q^{6} + 39 q^{8} + 27 q^{9}+O(q^{10}) \) 3 * q + q^2 + 9 * q^3 + 25 * q^4 - 11 * q^5 + 3 * q^6 + 39 * q^8 + 27 * q^9	\( 3 q + q^{2} + 9 q^{3} + 25 q^{4} - 11 q^{5} + 3 q^{6} + 39 q^{8} + 27 q^{9} + 55 q^{10} + 35 q^{11} + 75 q^{12} - 62 q^{13} - 33 q^{15} + 241 q^{16} - 48 q^{17} + 9 q^{18} + 202 q^{19} - 439 q^{20} - 7 q^{22} + 216 q^{23} + 117 q^{24} + 130 q^{25} - 274 q^{26} + 81 q^{27} + 53 q^{29} + 165 q^{30} + 95 q^{31} + 683 q^{32} + 105 q^{33} + 24 q^{34} + 225 q^{36} + 262 q^{37} + 398 q^{38} - 186 q^{39} - 21 q^{40} - 244 q^{41} + 360 q^{43} - 905 q^{44} - 99 q^{45} - 1056 q^{46} + 210 q^{47} + 723 q^{48} - 1378 q^{50} - 144 q^{51} - 324 q^{52} + 393 q^{53} + 27 q^{54} + 1031 q^{55} + 606 q^{57} - 1249 q^{58} - 1143 q^{59} - 1317 q^{60} + 70 q^{61} - 1059 q^{62} - 399 q^{64} - 472 q^{65} - 21 q^{66} - 628 q^{67} - 1944 q^{68} + 648 q^{69} + 318 q^{71} + 351 q^{72} - 988 q^{73} + 1002 q^{74} + 390 q^{75} + 2340 q^{76} - 822 q^{78} + 861 q^{79} - 175 q^{80} + 243 q^{81} - 124 q^{82} - 519 q^{83} + 1800 q^{85} - 3208 q^{86} + 159 q^{87} - 891 q^{88} - 1766 q^{89} + 495 q^{90} - 672 q^{92} + 285 q^{93} + 3294 q^{94} - 736 q^{95} + 2049 q^{96} - 19 q^{97} + 315 q^{99}+O(q^{100}) \) 3 * q + q^2 + 9 * q^3 + 25 * q^4 - 11 * q^5 + 3 * q^6 + 39 * q^8 + 27 * q^9 + 55 * q^10 + 35 * q^11 + 75 * q^12 - 62 * q^13 - 33 * q^15 + 241 * q^16 - 48 * q^17 + 9 * q^18 + 202 * q^19 - 439 * q^20 - 7 * q^22 + 216 * q^23 + 117 * q^24 + 130 * q^25 - 274 * q^26 + 81 * q^27 + 53 * q^29 + 165 * q^30 + 95 * q^31 + 683 * q^32 + 105 * q^33 + 24 * q^34 + 225 * q^36 + 262 * q^37 + 398 * q^38 - 186 * q^39 - 21 * q^40 - 244 * q^41 + 360 * q^43 - 905 * q^44 - 99 * q^45 - 1056 * q^46 + 210 * q^47 + 723 * q^48 - 1378 * q^50 - 144 * q^51 - 324 * q^52 + 393 * q^53 + 27 * q^54 + 1031 * q^55 + 606 * q^57 - 1249 * q^58 - 1143 * q^59 - 1317 * q^60 + 70 * q^61 - 1059 * q^62 - 399 * q^64 - 472 * q^65 - 21 * q^66 - 628 * q^67 - 1944 * q^68 + 648 * q^69 + 318 * q^71 + 351 * q^72 - 988 * q^73 + 1002 * q^74 + 390 * q^75 + 2340 * q^76 - 822 * q^78 + 861 * q^79 - 175 * q^80 + 243 * q^81 - 124 * q^82 - 519 * q^83 + 1800 * q^85 - 3208 * q^86 + 159 * q^87 - 891 * q^88 - 1766 * q^89 + 495 * q^90 - 672 * q^92 + 285 * q^93 + 3294 * q^94 - 736 * q^95 + 2049 * q^96 - 19 * q^97 + 315 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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